Cleanup model parameterization, approximation, and sensitivity

Patent metadata

Field	Value
Publication number	US-10352162-B2
Application number	US-201615005531-A
Country	US
Kind code	B2
Filing date	Jan 25, 2016
Priority date	Jan 23, 2015
Publication date	Jul 16, 2019
Grant date	Jul 16, 2019

Abstract

Methods and systems for generating and utilizing a proxy model that generates a pumping parameter as a function of contamination. The pumping parameter is descriptive of a pumpout time or volume of fluid to be obtained from a formation by a downhole sampling tool positioned in a wellbore extending into the formation. The contamination is a percentage of the fluid obtained by the downhole sampling tool that is not native to the formation. The proxy model is based on a true model that utilizes true model input parameters that include the pumping parameter, formation parameters descriptive of the formation, and a filtrate parameter descriptive of a drilling fluid utilized to form the wellbore. The output of the true model is the contamination as a function of the pumping parameter. The proxy model utilizes proxy model input parameters each related to one or more of the true model input parameters.

First claim

What is claimed is:

1. A method comprising:
operating a processing system comprising a processor and a memory to generate a proxy model by utilizing a true numerical model, wherein:
the true model utilizes a plurality of true model input parameters that include:
a pumping parameter descriptive of a pumpout time or volume of fluid to be obtained from a subterranean formation by a downhole sampling tool positioned in a wellbore extending into the subterranean formation;
a plurality of formation parameters descriptive of the subterranean formation; and
a filtrate parameter descriptive of a drilling fluid utilized to form the wellbore;

the output of the true model is contamination of the obtained fluid as a function of the pumping parameter;
the proxy model utilizes a plurality of proxy model input parameters each related to one or more of the true model input parameters;
the output of the proxy model is the pumping parameter as a function of the contamination; and
generating the proxy model comprises:
utilizing the true model to generate a plurality of true solutions for each of a plurality of different combinations of values of each of the plurality of true model input parameters; and
estimating fitting parameters of the proxy model utilizing the true solutions.

2. The method of claim 1 wherein the proxy model includes a regression function that approximates the proxy model output via interpolation utilizing the true solutions.

3. The method of claim 2 wherein the interpolation is kriging-based interpolation.

4. The method of claim 2 wherein the interpolation approximates the proxy model output as a plurality of low-order polynomials.

5. The method of claim 2 wherein the proxy model further includes a correlation function that weights the regression-approximated proxy model output utilizing the true solutions.

6. The method of claim 5 wherein the correlation function is at least one of a Gaussian function, an exponential function, and/or a spline function.

7. The method of claim 1 wherein the number of proxy model input parameters is less than the number of true model input parameters.

8. The method of claim 7 wherein the ones of the true model input parameters that are related to the proxy model input parameters each independently affect a cleanup behavior of the pumped fluid, and wherein others of the true model input parameters are not related to the proxy model input parameters and do not independently affect the cleanup behavior.

9. The method of claim 7 wherein each of the proxy model input parameters is dimensionless, and wherein each of the true model input parameters is not dimensionless.

10. The method of claim 7 wherein:
the true model input parameters include at least two of:
porosity of the subterranean formation;
absolute horizontal permeability of the subterranean formation;
absolute permeability anisotropy of the subterranean formation;
viscosity of the fluid to be obtained from the subterranean formation;
viscosity of the contamination;
depth of invasion of the contamination into the subterranean formation from the center of the wellbore;
diameter of the wellbore; and
the pumping parameter; and

the proxy model input parameters include at least one of:
a first ratio of the depth of contamination invasion to the wellbore diameter;
a second ratio of the viscosity of the fluid to be obtained from the subterranean formation to the contamination viscosity; and
the absolute permeability anisotropy of the subterranean formation.

11. The method of claim 1 wherein:
the processing system, the processor, and the memory are a first processing system, a first processor, and a first memory, respectively;
the first processing system is separate and distinct from a second processing system comprising a second processor and a second memory; and
the method further comprises operating one of the first and second processing systems to evaluate each of a plurality of sampling job scenarios utilizing the proxy model.

12. The method of claim 11 wherein evaluating the sampling job scenarios comprises:
randomly selecting values for each one of the proxy model input parameters that is unknown in the sampling job scenarios;
utilizing the proxy model to generate a plurality of estimates of the pumping parameter at a predetermined contamination utilizing the randomly selected values for each of the unknown proxy model input parameters; and
generating statistical estimates for the generated plurality of the pumping parameter estimates.

13. The method of claim 12 further comprising:
applying a global sensitivity analysis to the plurality of estimated pumping parameter values; and
identifying a formation or filtrate parameter that most influences the uncertainty in the estimated pumping parameter.

14. The method of claim 13 wherein identifying the parameter comprises quantifying a contribution of the parameter to the uncertainty in the estimated pumping parameter.

15. The method of claim 14 further comprising measuring the identified parameter.

16. The method of claim 1 further comprising:
obtaining values of the formation and filtrate parameters representative of the subterranean formation at a particular depth in the wellbore; and
using the proxy model and the obtained values to evaluate performance of the downhole sampling tool by estimating the pumping parameter value corresponding to a predetermined level of contamination of fluid to be obtained from the subterranean formation by the downhole sampling tool at the particular depth.

17. The method of claim 16 further comprising repeating the operating and using steps for at least two downhole sampling tools.

18. The method of claim 16 further comprising repeating the operating, obtaining, and using steps for at least two different depths within the wellbore.

19. A method of evaluating performance of a downhole sampling tool in a formation traversed by a wellbore comprising:
(a) generating a proxy model by utilizing a true numerical model of a downhole tool, wherein:
the true model utilizes a plurality of true model input parameters that include:
a pumping parameter descriptive of a pumpout time or volume of fluid to be obtained from a subterranean formation by a downhole sampling tool positioned in a wellbore extending into the subterranean formation;
a plurality of formation parameters descriptive of the subterranean formation; and
a filtrate parameter descriptive of a drilling fluid utilized to form the wellbore;

the output of the true model is contamination of the obtained fluid as a function of the pumping parameter;
the proxy model utilizes a plurality of proxy model input parameters each related to one or more of the true model input parameters;
the output of the proxy model is the pumping parameter as a function of the contamination; and
generating the proxy model comprises:
utilizing the true model to generate a plurality of true solutions for each of a plurality of different combinations of values of each of the plurality of true model input parameters; and
estimating fitting parameters of the proxy model utilizing the true solutions;

(b) obtaining values of formation and filtrate input parameters representative of formation at a particular depth; and
(c) using the proxy model for the downhole tool and the values of the input parameters to evaluate performance of a downhole sampling tool by estimating pumpout time or volume required to reach desired contamination level of a sampled fluid at a partic

Assignees

• Schlumberger Technology Corp

Inventors

• Kristensen Morten
• Ayan Cosan
• Lee Ryan Sangjun
• Chugunov Nikita

Classifications

• E21B49/10 Primary

  using side-wall fluid samplers or testers · CPC title